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Second-order analysis of piecewise linear functions with applications to optimization and stability  [PDF]
Boris S. Mordukhovich,M. Ebrahim Sarabi
Mathematics , 2015,
Abstract: This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit calculations of the second-order subdifferential for such functions, we establish relationships between nondegeneracy and second-order qualification for fully amenable compositions involving piecewise linear functions and obtain new applications of the developed second-order theory to full stability in composite optimization and constrained minimax problems, strong regularity of associate generalized equations and strong stability of stationary points in composition optimization, and Lipschitzian stability of parametric variational systems.
Polynomial Optimization with Applications to Stability Analysis and Control - Alternatives to Sum of Squares  [PDF]
Reza Kamyar,Matthew Peet
Mathematics , 2014,
Abstract: In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation Linear Techniques, Blossoming and Groebner basis methods, our main focus is on algorithms defined by Polya's theorem, Bernstein's theorem and Handelman's theorem. We first formulate polynomial optimization problems as verifying the feasibility of semi-algebraic sets. Then, we discuss how Polya's algorithm, Bernstein's algorithm and Handelman's algorithm reduce the intractable problem of feasibility of semi-algebraic sets to linear and/or semi-definite programming. We apply these algorithms to different problems in robust stability analysis and stability of nonlinear dynamical systems. As one contribution of this paper, we apply Polya's algorithm to the problem of H_infinity control of systems with parametric uncertainty. Numerical examples are provided to compare the accuracy of these algorithms with other polynomial optimization algorithms in the literature.
Parametric density-based optimization of partition in cluster analysis, with applications  [PDF]
E. Ostrovsky,L. Sirota,A. Zeldin
Statistics , 2013,
Abstract: We developed an optimal in the natural sense algorithm of partition in cluster analysis based on the densities of observations in the different hypotheses. These densities may be characterized, for instance, as the multivariate so-called "quasi-Gaussian distribution". We describe also the possible applications in technical diagnosis, demography and philology.
Matrix-Monotonic Optimization for MIMO Systems  [PDF]
Chengwen Xing,Shaodan Ma,Yiqing Zhou
Computer Science , 2013,
Abstract: For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables e.g., precoders, equalizers, training sequences, etc. are usually matrices. It is well known that matrix operations are usually more complicated compared to their vector counterparts. In order to overcome the high complexity resulting from matrix variables, in this paper we investigate a class of elegant multi-objective optimization problems, namely matrix-monotonic optimization problems (MMOPs). In our work, various representative MIMO optimization problems are unified into a framework of matrix-monotonic optimization, which includes linear transceiver design, nonlinear transceiver design, training sequence design, radar waveform optimization, the corresponding robust design and so on as its special cases. Then exploiting the framework of matrix-monotonic optimization the optimal structures of the considered matrix variables can be derived first. Based on the optimal structure, the matrix-variate optimization problems can be greatly simplified into the ones with only vector variables. In particular, the dimension of the new vector variable is equal to the minimum number of columns and rows of the original matrix variable. Finally, we also extend our work to some more general cases with multiple matrix variables.
Applications and Analysis of Bio-Inspired Eagle Strategy for Engineering Optimization  [PDF]
Xin-She Yang,M. Karamanoglu,T. O. Ting,Y. X. Zhao
Physics , 2014, DOI: 10.1007/s00521-013-1508-6
Abstract: All swarm-intelligence-based optimization algorithms use some stochastic components to increase the diversity of solutions during the search process. Such randomization is often represented in terms of random walks. However, it is not yet clear why some randomization techniques (and thus why some algorithms) may perform better than others for a given set of problems. In this work, we analyze these randomization methods in the context of nature-inspired algorithms. We also use eagle strategy to provide basic observations and relate step sizes and search efficiency using Markov theory. Then, we apply our analysis and observations to solve four design benchmarks, including the designs of a pressure vessel, a speed reducer, a PID controller and a heat exchanger. Our results demonstrate that eagle strategy with L\'evy flights can perform extremely well in reducing the overall computational efforts.
A Monotonic Precise Current DAC for Sensor Applications
P. Horsky
Radioengineering , 2008,
Abstract: In this paper a 17 bit monotonic precise current DAC for sensor applications is described. It is working in a harsh automotive environment in a wide temperature range with high output voltage swing and low current consumption. To guarantee monotonicity current division and segmentation techniques are used. To improve the output impedance, the accuracy and the voltage compliance of the DAC, two active cascoding loops and one follower loop are used. The resolution of the DAC is further increased by applying pulse width modulation to one fine LSB current. To achieve low power consumption unused coarse current sources are switched off. Several second order technological effects influencing final performance and circuits dealing with them are discussed.
Analysis of Optimization Techniques to Improve User Response Time of Web Applications and Their Implementation for MOODLE  [PDF]
Priyanka Manchanda
Computer Science , 2013,
Abstract: Analysis of seven optimization techniques grouped under three categories (hardware, back-end, and front-end) is done to study the reduction in average user response time for Modular Object Oriented Dynamic Learning Environment (Moodle), a Learning Management System which is scripted in PHP5, runs on Apache web server and utilizes MySQL database software. Before the implementation of these techniques, performance analysis of Moodle is performed for varying number of concurrent users. The results obtained for each optimization technique are then reported in a tabular format. The maximum reduction in end user response time was achieved for hardware optimization which requires Moodle server and database to be installed on solid state disk.
Traffic Analysis & Modeling in Wireless Sensor Networks and Their Applications on Network Optimization and Anomaly Detection  [PDF]
Qinghua Wang
Network Protocols and Algorithms , 2010,
Abstract: Wireless sensor network (WSN) has emerged as a promising technology thanks to the recent advances in electronics, networking, and information technologies. However, there is still a great deal of additional research required before it finally becomes a mature technology. This article concentrates on three factors which are holding back the development of WSNs. Firstly, there is a lack of traffic analysis & modeling for WSNs. Secondly, network optimization for WSNs needs more investigation. Thirdly, the development of anomaly detection techniques for WSNs remains a seldom touched area. Among these three factors, the understanding regarding the traffic dynamics within WSNs provide a basis for further works on network optimization and anomaly detection for WSNs.
Robust Monotonic Optimization Framework for Multicell MISO Systems  [PDF]
Emil Bj?rnson,Gan Zheng,Mats Bengtsson,Bj?rn Ottersten
Mathematics , 2011, DOI: 10.1109/TSP.2012.2184099
Abstract: The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasi-convex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.
Optimization and Development of Swellable Controlled Porosity Osmotic Pump Tablet for Theophylline
BP Rao, M Geetha, N Purushothama, U Sanki
Tropical Journal of Pharmaceutical Research , 2009,
Abstract: Purpose: To develop swellable controlled porosity osmotic pump tablet of theophylline and to define the formulation and process variables responsible for drug release by applying statistical optimization technique. Methods: Formulations were prepared based on Taguchi Orthogonal Array design and Fraction Factorial design for core and coating, respectively. The tablets were prepared by direct compression and wet granulation methods; spray coated with ethyl cellulose solution containing varying amounts of PEG 400 and plasdone. Drug release from the osmotic drug delivery system was studied using USP Type I paddle type apparatus. The membrane morphology of the delivery system was determined by scanning electron microscopy (SEM). Results: Optimization results indicated that the release rate of theophylline from the swellable controlled porosity osmotic pump tablet is directly proportional to the levels of osmotic agent, solubilizing agent and pore former in the tablet core and the membrane, respectively. SEM showed the formation of pores in the membrane through which drug release occurred. The best formulation showed 98.2 % drug release and complied with USP requirements. Conclusion: The results confirmed that the factors responsible for drug release were osmotic agents (core) and pore former (membrane). Also, the preparation of swellable controlled porosity osmotic pump tablet was facilitated by coating the core tablet with pore forming agent, thus eliminating the need for the more expensive laser drilling.
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